Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 4: Applications of Derivatives - Questions to Guide Your Review - Page 242: 14

Answer

See explanation below.

Work Step by Step

A cusp can be noticed on the graph at which the slope of a function $f(x)$ approaches $\infty$ from one side and $-\infty$ from the other side. Let us consider an example: $f(x)=x^{2/3}$ at $x=0$ $f'(x)=\dfrac{2}{3} \dfrac{1}{x^{1/3}}$ Thus, $\lim\limits_{x \to 0^{+}}f'(x) =+\infty$ and $\lim\limits_{x \to 0^{-}}f'(x) =-\infty$
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